# Form 4 Mathematics Paper 1 Section 2 Questions and Answers

In this session, we are going to solve Form 4 Mathematics paper 1 section 2 exam standard questions.

Answers are in video format.

Lessons (**16**) * SHARE*

- 1.
A cylindrical water tank is of diameter 7 metres and height 2.8 metres.
a) Find the capacity of the water tank in litres.
b) Six members of a family use 15 litres each per day. Each day
80 litres are used for cooking and washing
and a further 60 litres are wasted.
Find the number of complete days a full tank of water would last the family.
c) Two members of the family were absent for 90 days.

9m 50s - 2.
A helicopter is stationed at an airport H on a bearing #060^0# and 800 km from another airport P.
A third airport J is on a bearing of #140^0# and 1,200 km from H.
a) Determine
i) The distance between P and J.
ii) The bearing of P from J.
b) A jet flying at a speed of 1035 km/h left J towards P. The helicopter at H also took off towards P at the same time. Find the speed at which the helicopter

11m 37s - 3.
a) Given that the matrix# ((2,3),(3,4))#, find #A^-1#, the inverse of A.
b) Kariuki bought 400 goats and 600 sheep for a total of Kshs 1.7m. Maina bought 180 goats
and 240 sheep for a total of Kshs 720,000.
If the price of a goat is sh. X and that of a sheep is
shs y,
i) Form two equations to represent the above information.
ii) Use the matrix #A^-1# to find the price of one goat and one sheep.

13m 33s - 4.
In the figure below, TA is a tangent to the circle ABCD with centre O. Angle TAD = #48^0# and angle BOD =# 116^0#
Giving reasons calculate?
a) angle ACD
b) angle ABD
c) angle ADO
d) angle ACB
e) angle ATD

10m 32s - 5.
The table below gives some of the values of x and y for the function #y= 1/2x^2 + 2x + 1# in the interval #0 le x le 6#.
a) Use the values in the table to draw the graph of the
function on the grid provided.
b) i) Using the graph and the mid-ordinate rule with six (6) strips, estimate the area bounded by the
curve, the x – axis, the y- axis and the line x = 6.
ii) If the exact area of the region

10m 7s - 6.
The equation of a curve is given as
#y = x^3 – 3x + 2#.
Determine
a) The value of y when x = 2
b) The gradient of the curve at x = 3.
c) The turning points of the curve and their nature.

7m 0s - 7.
Nairobi and Eldoret are 600km apart. At 9.20a.m a lorry leaves Eldoret for Nairobi at a speed of 60km/hr. At 10.00a.m a car leaves Eldoret for Nairobi at a speed of 120km/hr. After 20 minutes of travel, the car develops a mechanical problem
which takes 20 minutes to repair. The car then proceeds with the journey at the same speed.
(a) Calculate the time the lorry arrived in Nairobi
(b) Find the

12m 34s - 8.
The table shows the marks obtained by 40 candidates in an examination

17m 19s - 9.
a).Solve the equation
#(y+3)/(24) = (1)/(y-2)#
b) A square carpet is laid on the floor of a room so that one of its sides is against a side of a room. It leaves strips of uncovered floor 1.5m wide along the two opposite sides and 2m wide along the
remaining side. If the area of the room is #72m^2#. Find
i) The dimension of the carpet
ii) The area of the uncovered floor.

8m 21s - 10.
The football team in school decided to raise ksh.3, 600 for a party. Each student was to contribute the same amount. However, before the contributions were made, five members of the football team decided to transfer to other schools. This
meant that the remaining contributors had to pay more to meet the same target.
a) If the increase in contribution per student was ksh.24. Taking the original

11m 47s - 11.
The figure below shows a solid structure in the shape of a frustum of a cone with a hemispherical bottom. The radius of the hemispherical part is 28cm and is equal to the radius of the bottom of the frustum. The
frustum has a top radius of 16cm and a height of 12cm. Use #pi=22/7#
a) Calculate to 2d.p.
i) The volume of the frustum.
ii) The volume of the solid.
b) Given that the solid has a mass of

9m 51s - 12.
Using a ruler and pair of compasses only.
a) Construct triangle ABC such that AB=6.3cm, BC = 7.2cm and angle ABC=#60^0#.
b) Measure the length AC.
c) Draw a circle that touches the vertices A, B and C.
d) Measure the radius of the circle.
e) Hence, calculate the area of the circle outside the triangle correct to one decimal place.

17m 40s - 13.
A line L1 passes through the points (-2, 3) and (-1, 6) and is perpendicular to L2 at (-1, 6).
a) Find the equation of L1.
b) Find the equation of L2 in the form ax + by
- c = 0 where a, b and c are constants.
c) Given that another line L3 is parallel to L1 and passes through point (1, 2), find the x and y intercepts of L3.
d) Find the point of intersection of L2 and L3.

8m 32s - 14.
The displacement of a particle S meters, t seconds after passing a fixed point O is given by
#S = 3 + 2t – 5t^2# Calculate:-
(a) The displacement of the particle 2 seconds later
(b) The time taken for the particle to return to O
(c) The maximum displacement of the particle
(d) The initial velocity of the particle

7m 43s - 15.
In the figure below OA = a, OB = b, OA: AE = 2: 3 and OB: OC = 1: 2
a).Express AC and BE in terms of a and b
i) AC
ii) BE
b). If DC = kAC and BD = mBE where k and m are scalars.
By expressing DC in two ways, determine the values of k and m.

9m 51s - 16.
Mr. Kamau, a salesman is paid a commission of 6% on goods worth over sh. 600,000. In addition he is paid a monthly salary of sh. 35,000.
(a) Calculate his total earnings in a month when his total sales was sh. 750,000.
(b) In the following month, the rate of commission was changed to x% but his monthly salary remained the same. If Mr. Kamau received a total monthly earning of sh. 100,000 for

9m 22s

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